The present invention relates to a family of gears having tooth profiles that are conjugate through most of the dedendum and addendum and a transition zone between the dedendum and addendum having no contact at the pitch circles. Additionally, the present invention also relates to a method for manufacturing gears having tooth profiles that are conjugate through most of the dedendum and addendum and that are not conjugate in the transition zone.
In the early Wildhaber-Novikov gears, as described by Chironis in “Design of Novikov Gears”, (a chapter of “Gear Design and Application”, McGraw-Hill, 1967, pp 124–135), the pinion is all-addendum and the gear tooth is all-dedendum. The transverse section tooth profile of the pinion is a convex circular arc, while that of the gear is a concave circular arc of slightly larger radius. These profiles are not conjugate. Contact takes place in each transverse section at one point only, usually near the middle of the profile. Consequently, there is no contact at the pitch point.
Later versions of Wildhaber-Novikov gears, also called “circular arc” gears, have profiles which lie both inside and outside the pitch circles. These profiles are known as doublemesh type. In each gear, the addendum is convex, either circular or approximately circular, and the dedendum profile is concave, either circular or approximately circular. The transverse section profiles of circular arc gears are not exactly circular as they are made conjugate to a basic cutter whose tooth profiles are circular arcs in either the transverse or the normal sections. The pinion and gear in such a gear pair are not conjugate with each other. Contact occurs in each transverse section at only one point in the addendum and one point in the dedendum. Typical examples of these types of gears are disclosed in U.S. Pat. No. 3,533,300 (Studer) and U.S. Pat. No. 3,855,874 (Honma). The circular arc gears disclosed in Studer are referred to therein as “nonconjugate”, while the circular arc gears disclosed in Honma are referred to therein as “of the so-called point contact type”.
In one respect, Studer or Honma type gears are similar to Convoloid gears disclosed in U.S. Pat. No. 6,101,892 (the '892 patent), incorporated herein in its entirety by reference, as each has no contact at the pitch circles. However, in other respects, Convoloid gears differ from Studer or Honma type gears. For example, Convoloid gears are conjugate through most of the addendum and most of the dedendum, with only a small non-conjugate section at the pitch circles, where no contact takes place; whereas, Wildhaber-Novikov and circular arc gears are not conjugate at any part of their profiles, and contact only occurs at one or two points of each transverse section.
The '892 patent describes full-depth Convoloid gears and additionally discloses a method for designing conjugate gear tooth profiles with specified relative curvatures. Further, the '892 patent discloses the existence of a section of each profile at the pitch circles, known as the transition zone, where no contact takes place. The transition zone is essential, because the relative curvature of profiles which are conjugate at the pitch point is given by the Euler-Savary equation, and cannot be specified by the profile designer.
Conjugate tooth profiles can be designed in the following manner. The dedendum of each tooth could be specified as any concave curve, and the addendum of the meshing gear designed as the corresponding conjugate profile. For example, the dedendum could be of the form y=Axb, where the y axis lies along a tooth space center-line, and the origin is at the root. Another example is the well-known cycloidal gear, where the dedendum is a hypocycloid, and the addendum is an epicycloid. In all such cases, it is possible to choose the dedendum profile as a concave curve, in such a manner that the conjugate addendum is convex. The relative curvature will then be mostly less than that of involute gears, even though it has not been specified directly by the profile designer.
One problem with the aforementioned design is that the relative curvature increases very rapidly near the pitch point, and the value at the pitch point is extremely high, due to the low pressure angle at that point. In the case of the cycloidal gears, the relative curvature is theoretically infinite. Thus, for these profiles to offer any benefit, they would need a transition zone at the pitch circles, similar to the profiles in the '892 patent.
The '892 patent describes the transition zone as a non-conjugate part of the profile, which does not come into contact with the meshing gear. The '892 patent is directed to any tooth profile which is conjugate through most of the dedendum and addendum, but has a small zone of no contact at the pitch circles. However, it is difficult to design tooth profiles that are taught by the '892 patent and that can be cut by conventional gear-cutting machines. Although a hob or a shaper cutter with a small protuberance at the pitch circle could possibly cut a gear which is non-conjugate at its pitch circle, the hob or shaper cutter would also undercut much of the conjugate gear tooth profile, leaving a profile which is useless. Accordingly there is a need for gears having a tooth profile with a transition zone that is non-conjugate at the pitch circle and that can be readily produced with conventional hobs or shaper cutters.